GEWU Magazine

Markov transition matrix and XXZ Hamiltonian1 questions

Constructing an integrable stochastic process associated with the twisted $D_2^{(2)}$ algebra

massive Ising field theory2 questions

First-principles derivation of Zamolodchikov's E8 S-matrix and of the infinite towers of higher-spin integrals of motion for the Ising model in a magnetic field
Complete analytic characterization of the universal scaling function of the two-dimensional Ising model in a magnetic field

matrix product operators（MPO）3 questions

matrix product states（MPS）2 questions

monodromy matrix2 questions

Circulation solutions of the Navier–Stokes and Euler equations relevant to natural disasters8 questions

Onsager algebra1 questions

Generalized Onsager algebras: irreducible modules beyond one-dimensional characters and the classified finite-dimensional cases, and inhomogeneous Serre presentations beyond symmetrizable Cartan matrices
Open for about 7 years

Onsager free energy2 questions

operator spreading2 questions

parafermion1 questions

Exact correlation functions and their disorder distributions in random free-parafermion chains

parafermionic CFT1 questions

Statistical interaction matrices for higher-rank level-2 parafermion theories and the resulting Rogers–Ramanujan-type q-identities

Perron–Frobenius property1 questions

Perron–Frobenius degrees of Perron numbers: which data control the minimal dimension of a non-negative integral matrix realization (Yazdi, Questions 5.1–5.4 and Remark 3.9)
Open for about 5 years

Pfaffian partition function2 questions

Poisson summation formula4 questions

Potts critical manifold3 questions

Potts critical exponents3 questions

Planar duality of the Potts model3 questions

Potts partition function3 questions

Potts latent heat1 questions

Ferromagnetic Potts model on the Betts (maple leaf) lattice: the q=4 magnetization-exponent anomaly and the unquantified weak first-order q=5 transition
Open for about 20 years

Potts and Ashkin-Teller Models4 questions

prethermalization2 questions

projected entangled-pair states（PEPS）2 questions

pseudoenergy2 questions

Non-perturbative dynamics of QCD6 questions

Phase structure of QCD at finite temperature and density and strongly coupled quark matter4 questions

quantum affine algebra4 questions

quantum determinant3 questions

quantum group

U_q(\mathfrak g)

3 questions

quantum KdV3 questions

quantum transfer matrix3 questions

quench action3 questions

Rapidity distribution3 questions

rapidity curve4 questions

rapidity line4 questions

reflection equation2 questions

Regularity, unitarity, and crossing3 questions

Constructing an integrable stochastic process associated with the twisted D2(2)D_2^{(2)}D2(2)​ algebra

First-principles derivation of Zamolodchikov's E8 S-matrix and of the infinite towers of higher-spin integrals of motion for the Ising model in a magnetic field

Complete analytic characterization of the universal scaling function of the two-dimensional Ising model in a magnetic field

Exact diagonalization of two-dimensional transfer operators (PEPOs) for three-dimensional models exhibiting phase transitions

Hopf-algebraic solvable unitary circuits: the bialgebra converse conjecture and the finite-exponent conjecture for C*-weak Hopf algebras

Controlled compression theory for local matrix product operators beyond first degree: second-degree operators, global truncation error, QR-iteration convergence, and precision-stable iterative compression

Completing boundary integrability from the fuzzy three-sphere: so2n\mathfrak{so}_{2n}so2n​-symmetric integrable matrix product states, sibling chains, and the quantum and holographic status of fuzzy-sphere defects

Finn–Vanicat Conjecture 4.1: the m→∞m\to\inftym→∞ limit of Koornwinder matrix-product states and an effective exact formula for the current cumulant generating function of the open ASEP

Q-operator, exceptional parameter loci, and correlation functions for the cyclic Bazhanov–Stroganov representations of the 6-vertex reflection algebra

Correlation-function building blocks for the open XXZ spin-1/2 chain with general integrable boundaries: the overlap factor, form factors, and the inverse problem

Open problems for the Coriolis-based gas dynamics of destructive atmospheric vortices: simulation fidelity, selection of a persistent vortex, planetary-rotation regimes, and energy feasibility of usage and mitigation

Robustness of the quasi-cyclostrophic regime predictions for tornado formation to realistic atmospheric processes

Tropical cyclone boundary layer shocks beyond the formation time: post-shock theory, shock-strength criteria, translating-storm geometry, and merger dynamics

Circulation sources of dust devil-like vortices: midlevel generation by convective organization and its extension to realistic dust devils

Modular analysis of tropical-cyclone structure beyond the boundary layer: the saturated inviscid core, eyed vortices, and the corner flow

Rigorous justification of the formal perturbation series for stationary powerful-tornado solutions of the reduced Navier–Stokes system, and the role of the Coriolis force in it

Extending the Li–Sinai renormalization-group blow-up theory for the 3D incompressible Navier–Stokes equations to non-axisymmetric fixed points and to real antisymmetric solutions

Self-consistent analytical modelling of tornado-like vortex velocity and surface-pressure fields across swirl ratios (the Gillmeier–Sterling–Hemida–Baker benchmark)

Generalized Onsager algebras: irreducible modules beyond one-dimensional characters and the classified finite-dimensional cases, and inhomogeneous Serre presentations beyond symmetrizable Cartan matrices

Direct derivation of the finite-size-scaling limit of the square-lattice Ising model on the open rectangle: the surface–corner scaling function and the critical lattice–CFT modular correspondence

Exact analytic theory of the finite-size expansions of the critical internal energy and specific heat of the two-dimensional Ising model with free boundaries

Operator spreading in single-particle quantum maps: the open-problem bundle of operator hydrodynamics, randomization, spectral-form-factor timescales, basis dependence, emergent classicality, and extensions to scars

Quasi-local soliton-gas mappings, ancestry algorithms, and sharp logarithmic operator-entanglement growth in interacting integrable quantum systems beyond the Rule 54 chain

Exact correlation functions and their disorder distributions in random free-parafermion chains

Statistical interaction matrices for higher-rank level-2 parafermion theories and the resulting Rogers–Ramanujan-type q-identities

Perron–Frobenius degrees of Perron numbers: which data control the minimal dimension of a non-negative integral matrix realization (Yazdi, Questions 5.1–5.4 and Remark 3.9)

Minimum number of Pfaffians representing the Ising partition function of a non-planar graph

Closed-form dimer-monomer generating function for a single monomer at an interior site of the square lattice (Wu's interior-monomer problem)

Sharp hypotheses and the maximal generalized theta-series class for the dimensionally continued Poisson summation formula

I-Bessel lattice sums in natural generality: convergence classification of plain sums, twisted Poisson summation without the divisibility hypothesis, and continuum limits at general scalings

Ground states of pair potentials with nonnegative compactly supported Fourier transform: the regimes below the threshold density, above close packing, and the bcc–fcc window

Rigorous foundations for the angular-averaged (Yakub-Ronchi) Ewald potential derivation: the lattice-sum identity S(k)=δ1,kS(k)=\delta_{1,k}S(k)=δ1,k​ and the Euler-Maclaurin-to-Poisson function class in three dimensions

Analytic theory of the critical-polynomial method for Potts critical manifolds: finite-size scaling exponents, antiferromagnetic zero loci, and the limits of applicability

Convergence, exactness, and the antiferromagnetic phase diagrams of the critical-polynomial method for two-dimensional Potts models

Exact critical manifold of the q-state Potts model on the kagome lattice and the convergence of its critical polynomials

Conformal field theories and critical exponents of the exact scattering solutions for the two-dimensional random-bond q-state Potts model

Upper critical dimension of the 3-state Potts model: pinning down dcrit(q=3)d_{\rm crit}(q=3)dcrit​(q=3) and the termination of its critical and tricritical fixed points

Magnetic critical exponent of the two-dimensional Potts model with long-range correlated bond disorder beyond leading perturbative order

Criticality of the self-dual point for random-cluster and Potts models on planar self-dual polygon configurations

Duality criterion for the three-state Potts antiferromagnet on plane quadrangulations: rigorous proof or classification of exceptions

Exact critical frontiers for the Potts and percolation models beyond the ferromagnetic triangular-decomposition class

Is the ferromagnetic Potts partition function AP-reducible to #BIS? The open converse in the Goldberg–Jerrum #BIS-hardness result for Tutte(q,γ), q>2, γ>0

Chromatic-count conjectures and the infinite-width limit of partition-function zeros for Potts models on honeycomb-lattice strips

Tutte-Beraha crossings of the partition-function-zero loci of the restricted Potts model on lattice strips (Chang-Shrock conjecture)

Ferromagnetic Potts model on the Betts (maple leaf) lattice: the q=4 magnetization-exponent anomaly and the unquantified weak first-order q=5 transition

Fixed-point structure of the pseudo-critical three-dimensional three-state Potts transition: the thermodynamic-limit scaling dimension of the subleading singlet ϵ′\epsilon'ϵ′ and the identity of the governing multicritical or complex fixed point

Nature of the phase-transition line of the three-dimensional Ashkin–Teller model: non-universality, wide crossover, or emergent-O(2) universality?

Defect magnetic critical behaviour of the two-dimensional Ashkin–Teller model with an asymmetric line defect

Criticality and conformally invariant scaling limits of the planar random-cluster model for 0<q<10<q<10<q<1 and for 1<q≤41<q\le41<q≤4, q≠2q\ne2q=2

Quantitative theory of fractionalized prethermalization in the driven one-dimensional Hubbard model: lifetime crossover, drive-class boundaries, and a controlled time-dependent Schrieffer-Wolff expansion

Meson-number-violating kinetic theory and interacting-meson prethermalization in confined one-dimensional quantum systems

Can projected entangled-pair states represent interacting (2+1)-dimensional chiral topological phases?

The complexity landscape of injective PEPS: the translation-invariant case, threshold sharpness, and the learning analogue

Exact derivation of the thermodynamic Bethe ansatz equations from the S-matrix/filling-fraction formalism for quantum gases

The general finite-volume boundary state: overlaps and excited-state g-functions in integrable QFT beyond diagonal scattering and bulk-only perturbations

Is vertex-dressing-function analyticity forced? The phase constraint behind confinement from the QCD effective charge

Rigorous establishment of the gluon-condensate route to confinement in Yang-Mills theory

Axion-meson mixing and the axion-photon coupling at next-to-next-to-leading order in U(3) chiral perturbation theory

Universality class of the chiral phase transition in (2+1)-flavor QCD and the fate of effective UA(1)U_A(1)UA​(1) symmetry at Tc0T_c^0Tc0​ in the chiral limit

Open questions on Cheshire θ\thetaθ terms: UV origin, the Skyrme-current–η′\eta'η′ coupling in large-NcN_cNc​ QCD, and their physical consequences

Completing the anomaly-matching proof of chiral symmetry breaking in QCD-like theories: the heavy-quark continuity gap for Nf<pmin⁡N_f<p_{\min}Nf​<pmin​ and generalization beyond SU(Nc)SU(N_c)SU(Nc​) fundamentals

Reentrant first-order deconfinement transition at high baryon density in heavy-quark lattice QCD and the connection between heavy- and light-quark first-order boundaries

Microscopic determination of the in-medium quark couplings of cold dense quark matter — vector repulsion, flavor-non-singlet vector couplings, and diquark coupling — from nonperturbative gluon exchange

Quantitative phase structure of QCD at finite temperature and chemical potential: partial deconfinement, baryon condensation, and the QCD critical point

Mapping the chiral-spin-symmetric (stringy-fluid) band of the QCD phase diagram: the quantitative upper boundary at finite baryon chemical potential, its fate at large density, and the order of the inter-regime transitions

Simplicity of tensor products of Kirillov-Reshetikhin modules for the non-nested interval collections of Kanakubo-Koshevoy-Nakashima (Conjecture 7.11)

Completeness of the Bethe ansatz and rationality of Baxter polynomials for twisted transfer-matrices of quantum affine algebras

Freidel–Maillet type presentations beyond the positive part of Uq(sl2^)U_q(\widehat{sl_2})Uq​(sl2​​): the equitable-type presentation of the full quantum affine algebra, higher-rank extensions, and the complete Hopf isomorphism between its Drinfeld–Jimbo and Drinfeld realizations

Irreducibility criterion for tensor products of a snake module with an arbitrary simple module over quantum affine slk\mathfrak{sl}_kslk​ (Bittmann–Li Conjectures 5.10 and 5.6)

Commutativity of quantum elementary symmetric polynomials in half-quantum algebras

Commutativity of antidiagonal quasi-determinants in the reflection equation algebra for arbitrary rank (Talalaev's Hypothesis 2.6)

Centrality of the quantum hyperdeterminant: constructing the quotient algebra of quantum hypermatrices in which Det⁡q\operatorname{Det}_qDetq​ becomes central

The alternating universal K-matrix for the q-Onsager algebra: construct a universal K-matrix for the alternating central extension AqA_qAq​ from solutions of a universal Freidel-Maillet type equation, or prove that none exists

Weyl-group invariance of the quantum group image in the cluster realization of higher Teichmüller theory

Higher Frobenius–Schur indicators of small quantum groups: effective formulas for uq(g)u_q(\mathfrak{g})uq​(g) beyond sl2\mathfrak{sl}_2sl2​ and the gcd-divisibility of νn(H)\nu_n(H)νn​(H)

All-orders shifted symmetric structure of the quantum KdV eigenvalues (Conjecture 1.9 of van Ittersum–Ruzza)

Extend the meromorphic-differential/double-ramification correspondence from the trivial and Hodge CohFTs to general cohomological field theories satisfying the strata vanishing conditions

Irreducibility, genus, and global geometry of the spectral curves of the quantum KdV hierarchy

Correlation functions of the integrable SU(n)SU(n)SU(n) spin chain: analytic three-site evaluation, extension to m≥4m\ge 4m≥4 and n>3n>3n>3, and finite-temperature computation

Completing the rigorous low-temperature spectral theory of the quantum transfer matrix of the massless XXZ spin-1/2 chain

Constructing an integrable stochastic process associated with the twisted $D_2^{(2)}$ algebra

Completing boundary integrability from the fuzzy three-sphere: $\mathfrak{so}_{2n}$ -symmetric integrable matrix product states, sibling chains, and the quantum and holographic status of fuzzy-sphere defects

Finn–Vanicat Conjecture 4.1: the $m\to\infty$ limit of Koornwinder matrix-product states and an effective exact formula for the current cumulant generating function of the open ASEP

Rigorous foundations for the angular-averaged (Yakub-Ronchi) Ewald potential derivation: the lattice-sum identity $S(k)=\delta_{1,k}$ and the Euler-Maclaurin-to-Poisson function class in three dimensions

Upper critical dimension of the 3-state Potts model: pinning down $d_{\rm crit}(q=3)$ and the termination of its critical and tricritical fixed points

Fixed-point structure of the pseudo-critical three-dimensional three-state Potts transition: the thermodynamic-limit scaling dimension of the subleading singlet $\epsilon'$ and the identity of the governing multicritical or complex fixed point

Criticality and conformally invariant scaling limits of the planar random-cluster model for $0<q<1$ and for $1<q\le4$ , $q\ne2$

Universality class of the chiral phase transition in (2+1)-flavor QCD and the fate of effective $U_A(1)$ symmetry at $T_c^0$ in the chiral limit

Open questions on Cheshire $\theta$ terms: UV origin, the Skyrme-current– $\eta'$ coupling in large- $N_c$ QCD, and their physical consequences

Completing the anomaly-matching proof of chiral symmetry breaking in QCD-like theories: the heavy-quark continuity gap for $N_f<p_{\min}$ and generalization beyond $SU(N_c)$ fundamentals

Freidel–Maillet type presentations beyond the positive part of $U_q(\widehat{sl_2})$ : the equitable-type presentation of the full quantum affine algebra, higher-rank extensions, and the complete Hopf isomorphism between its Drinfeld–Jimbo and Drinfeld realizations

Irreducibility criterion for tensor products of a snake module with an arbitrary simple module over quantum affine $\mathfrak{sl}_k$ (Bittmann–Li Conjectures 5.10 and 5.6)

Centrality of the quantum hyperdeterminant: constructing the quotient algebra of quantum hypermatrices in which $\operatorname{Det}_q$ becomes central

The alternating universal K-matrix for the q-Onsager algebra: construct a universal K-matrix for the alternating central extension $A_q$ from solutions of a universal Freidel-Maillet type equation, or prove that none exists

Higher Frobenius–Schur indicators of small quantum groups: effective formulas for $u_q(\mathfrak{g})$ beyond $\mathfrak{sl}_2$ and the gcd-divisibility of $\nu_n(H)$

Correlation functions of the integrable $SU(n)$ spin chain: analytic three-site evaluation, extension to $m\ge 4$ and $n>3$ , and finite-temperature computation

The atom-loss functional $F[\rho](k)$ of the one-dimensional Bose gas: evaluation beyond the asymptotic regimes and loss-driven rapidity dynamics

The generalized order-parameter function $G_{pq}(r)$ of the solvable chiral Potts model at arbitrary rapidities

Discrete-spin solutions of the star-triangle relation from root-of-unity limits beyond the $\mathbb{Z}_N$ -symmetric family

First-principles ODE/IQFT derivation and the quantization-condition conjecture for the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ -invariant open boundary conditions

Root locations of the XXZ Bethe Ansatz equations: the unproven intermediate anisotropy regime and the $N\ge 3$ magnon sectors

Descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras: analytic proofs of the all- $n$ Yang-Baxter conjectures and the Fateev-Zamolodchikov limit